Posts on: Physics
Chapter 6 of Evidence, Decision and Causality presents another alleged counterexample to CDT, involving a bet on the measurement of entangled particles.
The setup is Bohm's version of the Einstein, Podolsky, Rosen experiment, as described in Mermin (1981) (see esp. pp.407f.).
We have prepared a "source" S that, when activated, emits two entangled spin 1/2 particles, travelling towards causally isolated detectors A and B. The detectors contain Stern-Gerlach magnets whose orientation is controlled by a switch with three settings (1, 2, 3). When the switches on the two detectors are on the same setting, the magnets have the same orientation. Detector A flashes 'y' if the measured spin is along the magnetic field and 'n' otherwise. Detector B uses the opposite convention, flashing 'n' if the measured spin is along the magnetic field.
It is tempting to think that there is nothing more to physical
quantities than their nomic role: that to have a certain mass just is
to behave in such-and-such a way under such-and-such conditions.
But it is also tempting to think that the "Galilean equivalence" of
inertial mass and gravitational mass is a true identity; i.e.,
that
Inertial mass = gravitational mass.
However, the role associated with "inertial mass" is completely
different from the role associated with "gravitational mass". So if
having such-and-such inertial mass is having the relevant
dispositions associated with "inertial mass", and likewise for
gravitational mass, then the Galilean equivalence could not be an
identity. It would rather state an empirical law, according to which
two distinct quantities always have the same value.
If you spin a wheel of fortune, the outcome -- red or black -- depends
on the speed with which you spin. As you increase the speed,
the outcome quickly cycles through the two possibilities red and
black. As a consequence, any reasonably smooth probability distribution
(or frequency distribution) over initial speed determines an
approximately equal probability (frequency) for red and black. Here is
an example of such a distribution, taken from Strevens.
I've been asked to review Michael Strevens's new book,
Tychomancy. This motivated me to have another look at his
earlier book Bigger than Chaos.
The aim of Bigger than Chaos is to explain how apparently
chaotic interactions in highly complex systems often give rise to
simple large-scale regularities, such as the laws of thermodynamics,
the stability of predator/prey population levels, or the economic
cycle. The basic explanatory strategy, which Strevens calls enion
probability analysis (EPA), consists in aggregating the
probabilistic dynamics for the individual components of a complex
system into a probabilistic dynamics for macro-level features of the
system.
Many of our best scientific theories make only probabilistic
predications. How can such theories be confirmed or disconfirmed by
empirical tests?
The answer depends on how we interpret the
probabilistic predictions. If a theory T says 'P(A)=x', and we
interpret this as meaning that Heidi Klum is disposed to bet on A at
odds x : 1-x, then the best way to test T is by offering bets to Heidi
Klum.
Nobody thinks this is the right interpretation of probabilistic
statements in physical theories. Some hold that these statements are
rather statements about a fundamental physical quantity called
chance. Unlike other quantities such as volume, mass or charge,
chance pertains not to physical systems, but to pairs of a time and a
proposition (or perhaps to pairs of two propositions, or to triples of
a physical system and two propositions). The chance quantity is
independent of other quantities. So if T says that in a certain type
of experiment there's a 90 percent probability of finding a particle
in such-and-such region, then T entails nothing at all about particle
positions. Instead it says that whenever the experiment is carried
out, then some entirely different quantity has value 0.9 for a certain
proposition. In general, on this interpretation our best theories say
nothing about the dynamics of physical systems. They only make
speculative claims about a hidden magnitude independent of the
observable physical world.
There has been some discussion recently about whether propositions
are true or false absolutely, or only relative to a possible world, or
relative to a world and a time. What hasn't been considered, to my
knowledge, is whether propositions are true or false only relative to
a branch of the wave function of the universe.
For example, suppose we shoot a photon at a half-silvered
mirror. It then enters into a superposition of passing through
and getting reflected: these are the two "branches" of the
superposition. More precisely, it is not the photon that enters into
the superposition, but the entire setup, and there are actually many
more branches, corresponding to various precise paths the photon can
take. Moreover, these branches are only the position branches
of the superposition -- there are other branches of the same
superposition, corresponding to resolutions of other properties.
This paper (recently
featured on the
physics arXiv blog) argues that if the universe never comes to an
end, then the universe will probably come to an end within the next 5 billion
years. The reasoning, as far as I can tell, goes roughly like
this.
First, define the probability of an event of type A given an event
of type B as the total number of A events over the number of B
events. If the universe is infinite, then the total number of A events
and B events will often be infinite. But infinity over infinity isn't
well-defined. So to have well-defined probabilities, the relevant
counts of A and B events must be restricted, e.g. to a finite initial
segment of the universe.
One of the novelties in Richard Jeffrey's "Logic of Decision"
(1965) was to unify the space over which probabilities and values are
defined: both probability and desirability are distributed over the
space of possible worlds, of ways things might be. By contrast, in
earlier theories like that of Savage, probabilities were defined over
states (or events) and utilities over
consequences, which were taken to be distinct kinds of
things. Technically, this difference between Savage and Jeffrey isn't
terribly important as long as anything an agent may care about can be
found in the set of 'consequences'. However, the distinction and the
labeling in Savage's treatment carries a danger to overlook the
complexity of human values. This has, I believe, led to a number of
serious mistakes.
...in the latest issue of Nature, some physicists published an empirical refutation of
'realism' -- a viewpoint according to which an external reality exists independent of observation.
They also advocate considering
the breakdown of [...] Aristotelian logic, counterfactual definiteness, absence of actions into the past or a world that is not [sic] completely deterministic.
As far as I can tell, what they actually found is evidence against certain local hidden-variable theories that survived Bell's inequalities. Aristotelian syllogisms and realism (in the above sense) seem to be thrown out by the principle that if you throw out the bath water, you might as well throw out the whole bathroom.
When sometime between 1986 and 2001, Lewis accepted (a certain version of) standard quantum physics, did he thereby accept that Humean Supervenience is false? I'm not sure. My knowledge of quantum physics ("knowledge" in the sense of "probably false, unjustified guesses" rather than "true, justified beliefs") doesn't suffice to see through this with any confidence. Anyway, here's some thoughts.
Humean Supervenience is the hypothesis that in worlds like ours, all
truths supervene on the spatiotemporal distribution of fundamental
properties at spacetime points. This appears to contradict what quantum physics says about entangled states: if two electrons are suitably entangled, their combined state is a superposition of X-spin(electron 1)=up & X-spin(electron 2)=down and X-spin(electron 1)=down & X-spin(electron 2)=up (![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5Csqrt%7B1%2F2%7D%7C%5Cmbox%7BX-up%7D%5Crangle_1%7C%5Cmbox%7BX-down%7D%5Crangle_2+-+%5Csqrt%7B1%2F2%7D%7C%5Cmbox%7BX-down%7D%5Crangle_1%7C%5Cmbox%7BX-up%7D%5Crangle_2)
, or so), which is not determined by any local qualities of the individual electrons: there are no spin states A and B such that whenever some electron is in A and another one in B, then their mereological fusion is in this entangled state. So Humean Supervenience is false.
What can we say about physical systems when they are not in an eigenstate of a certain property? For instance, what can we say about an electron's x-spin when it is in a superposition of 'up' and 'down'?
We can say that a measurement of the property will (or rather, would) deliver such and such results with such and such probability. Most physicists apparently think that this is more or less all we can say. In particular, they argue that we should not interpret the superposition state as something like "the probability that the electron now actually has x-spin up is 0.5": having x-spin up (or down) requires being in an eigenstate of x-spin, but the electron is in no such eigenstate; thus the electron definitely has neither x-spin up nor x-spin down; it is in a superposition state, and that's all there is.
I've often read that thermodynamic entropy is some measure of disorder, so that tyding up our rooms means working against the second law of thermodynamics. For example, in section 9.3 of his book Space, Time and Quanta, Robert Mills demonstrates that if we put 10^20 toys back on the shelf, that decreases the total cosmic entropy by 0.02 J/K. He then suggests that this doesn't actually violate the second law because in the process of putting back the toys we use up energy and thereby increase total entropy by much more than 0.02 J/K.
So I don't see any means to escape the conclusion that given mereological universalism, some things trivially move faster than light. Lots of things, in fact. Perhaps that's less troublesome than I thought because these things don't actually violate any physical laws.
For instance, I guess the principle that physics looks the same for all things that move with constant speed relative to each other has to be restricted to things with speed < c anyway. (At least Lorentz transformation doesn't make much sense if v = c.) If so, the exclusion of faster-than-light fusions from the principle is already built in and we don't need to worry about e.g. what such a fusion's proper time might be.